A statistical distribution published by William Gosset in 1908. His employer,
Guinness Breweries, required him to publish under a pseudonym, so he
chose "Student". Given N independent measurements, let

where M is the population mean,μ
is the sample mean, and s is the sample variance.

Student's t-distribution is defined as the distribution of the random
variable t which is - very loosely - the "best" that we can
do not knowing the true standard deviation of the sample. It has the
PDF:

The Student's t-distribution takes a single parameter: the number of
degrees of freedom of the sample. When the degrees of freedom is one
then this distribution is the same as the Cauchy-distribution. As the
number of degrees of freedom tends towards infinity, then this distribution
approaches the normal-distribution. The following graph illustrates how
the PDF varies with the degrees of freedom ν: